{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,25]],"date-time":"2025-09-25T18:11:17Z","timestamp":1758823877309},"reference-count":4,"publisher":"World Scientific Pub Co Pte Lt","issue":"04","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Discrete Math. Algorithm. Appl."],"published-print":{"date-parts":[[2014,12]]},"abstract":"<jats:p> Let G be a connected graph. Suppose that a fire breaks out at some vertex. A firefighter starts to protect vertices. At each time interval, the firefighter protects k vertices not yet on fire. At the end of each time interval, the fire spreads to all the unprotected vertices that have a neighbor on fire. The k-surviving rate \u03c1<jats:sub>k<\/jats:sub>(G) of G is the average proportion of saved vertices, if the starting vertex of the fire is chosen uniformly at random. A graph G is called k-good if there is a constant c &gt; 0 such that \u03c1<jats:sub>k<\/jats:sub>(G) \u2265 c. We study structural properties of planar graphs and show that planar graphs are 3-good. <\/jats:p>","DOI":"10.1142\/s1793830914500529","type":"journal-article","created":{"date-parts":[[2014,8,4]],"date-time":"2014-08-04T03:06:19Z","timestamp":1407121579000},"page":"1450052","source":"Crossref","is-referenced-by-count":6,"title":["Structural properties and surviving rate of planar graphs"],"prefix":"10.1142","volume":"06","author":[{"given":"Jiangxu","family":"Kong","sequence":"first","affiliation":[{"name":"School of Mathematical Science, Xiamen University, Fujian 361005, P. R. China"}]},{"given":"Lianzhu","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Mathematical Science, Xiamen University, Fujian 361005, P. R. China"}]},{"given":"Weifan","family":"Wang","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Zhejiang Normal University, Jinhua 321004, P. R. China"}]}],"member":"219","published-online":{"date-parts":[[2014,10,10]]},"reference":[{"key":"rf1","first-page":"1814","volume":"23","author":"Cai L.","year":"2009","journal-title":"SIAM J. Discrete Math."},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1002\/jgt.21673"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1016\/j.tcs.2011.10.002"},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1016\/j.tcs.2010.06.009"}],"container-title":["Discrete Mathematics, Algorithms and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S1793830914500529","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T12:46:49Z","timestamp":1565095609000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S1793830914500529"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,10,10]]},"references-count":4,"journal-issue":{"issue":"04","published-online":{"date-parts":[[2014,10,10]]},"published-print":{"date-parts":[[2014,12]]}},"alternative-id":["10.1142\/S1793830914500529"],"URL":"https:\/\/doi.org\/10.1142\/s1793830914500529","relation":{},"ISSN":["1793-8309","1793-8317"],"issn-type":[{"value":"1793-8309","type":"print"},{"value":"1793-8317","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014,10,10]]}}}